Question

determine o perimetro do quadrilatero cujos vertices A,B,C e D tem as seguintes coordenadas A(1 5) B(-2 1) C(4 1) D(1 4)

Answer 1

Achando a distância entre dois pontos 

$D = \sqrt{( x_{2}- x_{1} )^2+( y_{2} - y_{1})^2} \\ \\ \\ AB= \sqrt{(-2-1)^2+(1-5)^2} = \sqrt{(-3)^2+(-4)^2} = \sqrt{9+16} = \sqrt{25} =5 \\ \\ \\ CD= \sqrt{(1-4)^2+(4-1)^2} = \sqrt{(-3)^2+3^2} = \sqrt{9+9} = \sqrt{18} = \sqrt{3^2.2} \\ \\ \\ =3 \sqrt{2} \\ \\ AC= \sqrt{(4-1)^2+(1-5)^2} = \sqrt{3^2+(-4)^2} = \sqrt{9+16} = \sqrt{25}=5 \\ \\ \\ BD= \sqrt{(1-(-2))^2+(4-1)^2} = \sqrt{3^2+3^2} = \sqrt{18} =3 \sqrt{2}$

per+imetro=$5+3 \sqrt{2} +5+3 \sqrt{2} =10+6 \sqrt{2}$